A240868 Number of partitions of n into distinct parts of which the number of even parts is not a part and the number of odd parts is not a part.

0, 0, 1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 7, 8, 10, 10, 16, 15, 23, 19, 32, 27, 44, 36, 60, 50, 80, 67, 103, 92, 137, 124, 174, 167, 224, 221, 284, 292, 362, 382, 453, 497, 574, 641, 715, 821, 897, 1046, 1117, 1323, 1396, 1664, 1729, 2082, 2151, 2591, 2660, 3213

Offset

0,5

Links

Table of n, a(n) for n=0..57.

Example

a(9) counts these 4 partitions:  9, 72, 63, 54.

Mathematica

z = 70; f[n_] := f[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &];
    t1 = Table[Count[f[n], p_ /; MemberQ[p, Count[Mod[p, 2], 0]]], {n, 0, z}] (* A240862 *)
    t2 = Table[Count[f[n], p_ /; MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}] (* A240863, *)
    t3 = Table[Count[f[n], p_ /; MemberQ[p, Count[Mod[p, 2], 0]] && MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}] (* A240864 *)
    t4 = Table[Count[f[n], p_ /; MemberQ[p, Count[Mod[p, 2], 0]] || MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}] (* A240865 *)
    t5 = Table[Count[f[n], p_ /; MemberQ[p, Count[Mod[p, 2], 0]] && ! MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}] (* A240866 *)
    t6 = Table[Count[f[n], p_ /; ! MemberQ[p, Count[Mod[p, 2], 0]] && MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}] (* A240867 *)
    t7 = Table[Count[f[n], p_ /; ! MemberQ[p, Count[Mod[p, 2], 0]] && ! MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}] (* A240868 *)

Crossrefs

Cf. A240862, A240863, A240864, A240865, A240866, A240867; for analogous sequences for unrestricted partitions, see A240573-A240579.

Sequence in context: A120178 A120179 A032739 * A029149 A080570 A163001

Adjacent sequences: A240865 A240866 A240867 * A240869 A240870 A240871

Keyword

nonn,easy

Author

Clark Kimberling, Apr 14 2014

Status

approved